Frustum of a Right Circular Cone Formula
When we chop off the top of a right circular cone what we get is known as the frustum of a right circular cone. Its altitude is defined as the distance between the two flat surfaces. It is denoted by ‘h’. The elements of the frustum are denoted by ‘L’. It is also known as the slant height of the Frustum. The two flat surfaces are known as the two bases of the frustum. These areas can be defined as A_{1} and A_{2}. We use the frustum of a right circular cone formula for finding the total surface area for the frustum of a right circular cone, the lateral surface area for the frustum of a right circular cone and, the volume for the frustum of a right circular cone. Let us learn more about the frustum of a right circular cone formula along with solved examples.
What is Frustum of a Right Circular Cone Formula?
There are three general formulas for the frustum of a right circular cone, as given below.
 Formulas for the total surface area of a frustum of a cone.
Total surface area = \(\pi L(R + r)+\pi R^2+\pi r^2\)
 Formulas for lateral surface area for frustum of a right circular cone
Lateral Surface Area = π(r + R)L
 Formulas for volume for frustum of a right circular cone
Volume = \(\dfrac{1}{3}\pi (R^2 + r^2+Rr)h\)
where,
r and R = Radius of the bases
h = Height
L = Slant height
Solved Examples Using Frustum of a Right Circular Cone Formula

Example 1:
Find the lateral surface area of the frustum of a right circular cone whose radius of the bases are 12 units and 15 units respectively and slant height is 10 units.
Solution:
To Find: lateral surface area of the frustum of a right circular cone.
Given: r = 12 units
R = 15 units
L = 10 unitsNow, using the formula for the lateral surface area of the frustum of a right circular cone.
Lateral Surface Area for frustum of a right circular cone = π(r + R)L
= π (12 + 15)10
= π (27)10
= π (270)
= 848.23 square units
Answer: lateral surface area of the frustum of the right circular cone is 848.23 square units.

Example 2:
Find the volume of the frustum of a right circular cone whose radius of the bases are 10cm and 12cm respectively and height is 15 cm.
Solution:
To Find: volume of the frustum of a right circular cone.
Given:r = 10cm
R = 12cm
h = 15cmNow, using the formula for the volume of the frustum of a right circular cone.
\(\text{Volume for frustum of a right circular cone } = \dfrac{1}{3}\pi (R^2 + r^2+Rr)h\)
= \(\dfrac{1}{3}\pi (12^2 + 10^2 + 10\times12)15\)
= \(\dfrac{1}{3}\pi (144+100+120)15\)
= \(\dfrac{1}{3}\pi(364)15\)
= \(\dfrac{1}{3}\pi 5460\)
= π(1820)
= 5717.7cm^{3}
Answer: The volume of the frustum of the right circular cone is = 5717.7cm^{3}